A rubber composition for tire members is comprised of rubber, in which carbon black and a vulcanization agent, are compounded, and therefore, is high in viscosity. Further, at high temperatures, the rubber is cross-linked, and therefore, there are limits to the molding temperature. For example, it is difficult to coextrude a high molding temperature ethylene vinyl alcohol copolymer (EVOH) (molding temperature: 190 to 250° C.) to make a laminate of an EVOH thin film/rubber composition, and therefore a process of forming a single layer of a thin film of EVOH, followed by laminating with a rubber composition is not possible. No industrial method of production of an EVOH thin film/rubber composition laminate has yet been established. No prior art documents of such art are known.